The present invention relates to spectrometry and more particularly to an electrostatic electron spectrometry apparatus that includes a toroidal spectrometer configured for second order focusing at a detector plane. Toroidal electron energy spectrometers have been used for angular photoemission studies, electron scattering experiments, and the capture of the backscattered electron (BSE) spectrum in the Scanning Electron Microscope (SEM). Toroidal Spectrometers have the desirable feature of possessing rotational symmetry, and are naturally able to collect electrons in the full 2π azimuthal direction. However, their focusing properties are usually based upon first-order optics, which makes their attainable energy resolution (for a given entrance angular spread) inferior to other types of 2π radian collection spectrometers such as the Cylindrical Mirror Analyzer (CMA), commonly used in Scanning Auger Microscopy (SAM).
At its second-order focusing condition (only possible at an entry angle of 42.3°), the CMA energy resolution has a cubic dependence on input angular spread, approximately 1.38 Δθ3 for acceptance angles between ±6°, indicating that its energy resolution is limited by 3rd order spherical aberration. This gives an average theoretical relative energy resolution (100′ ΔE/E) of around 0.155%. Assuming a cosine distribution with respect to the polar angle θ (measured relative to the z-axis) and 2π radian emission in the azimuthal angular direction, the total theoretical transmission is proportional to sin(2θ), around 20% for ±6°. In practice, grids are used at the spectrometer entrance and exit which typically lower the transmission to around 14%. In contrast, toroidal spectrometers (non-retarded) have a theoretical energy resolution of around 0.25% at ±3° acceptance angles (around 10% transmission). This value has been predicted by simulation for both a toroidal spectrometer in photoemission applications, and a toroidal backscattered electron spectrometer for the SEM. The energy resolution of 0.25% at ±3° acceptance angles is also comparable to the one usually quoted for the Concentric Hemispherical Analyser (CHA) on its Gaussian focal plane, given by Δθ2.
There are of course other advantages of toroidal spectrometers that make up for inferior energy resolution caused by first-order focusing. A toroidal spectrometer, much like a Concentric Hemispherical Analyser (CHA), can be biased to lower the kinetic energy of electrons that pass through it, thereby improving its relative energy resolution. Also like hemispherical spectrometers, toroidal spectrometers can simultaneously record different emission energies, capturing a parallel energy window of up to 15% (±7%) of the pass energy. These things are not easy to achieve with the CMA. In practice, some other constraints make the CMA difficult to use for many applications, such as its sensitivity to specimen placement.
A spectrometry apparatus according to the present invention includes a fully 2π radian collection second-order focusing toroidal spectrometer, which is based upon obtaining an intermediate focus in the r-z plane. This allows for second-order spherical aberration contributions accumulated before and after the intermediate focus to cancel, since electrons with emission angles to either side of the central ray gain spherical aberration are of opposite sign. The inventors have investigated a range of different geometrical designs, the best of which have the following simulated predictions: second-order focusing with an expected energy resolution of 0.146% for acceptance angles between ±6°, comparable to the theoretically best resolution-transmittance of the CMA; parallel energy acquisition where the increase in energy resolution with respect to the band centre rises by less than a factor of 2 for energies that lie within ±4% of the pass energy; a maximum input angular spread of ±10° and a maximum parallel energy band width of ±15% (30% total) of the pass energy; retarding/accelerating field mode of operation without the need to incorporate auxiliary lenses; and depending on the precise application, no working distance limitations.
For parallel energy detection, the detection plane can be positioned on the surface of a shallow cone whose slanting side makes an angle of around 26.4° with respect to the horizontal. A multi-channel array of flat strip detectors in the azimuthal direction is not expected to significantly degrade the energy resolution, typically less than 5% for 40 such detectors. For low energy electrons, typically less than 50 eV, electrons can be mirrored on to a flat plate detector located below the specimen after they pass through the spectrometer. The energy resolution is only marginally degraded by doing this, predicted to be 0.196% at the centre pass band energy (for an input angular spread of ±6°).
To simulate the performance of a spectrometer according to the present invention, finite element programs were used to solve for two-dimensional rotationally symmetric electrostatic field distributions on a polar mesh. Numerical ray tracing of electrons through these field distributions were then plot using bi-cubic interpolation and the 4th-order Runge-Kutta method. The meshes were graded so that smaller mesh cells were used within the centre region between the deflection plates. The size of each adjoining mesh cell was increased by 10% in the radial direction, and mesh cells mid-way between the plates were selected to be typically 276 smaller than those at electrode boundaries. The base mesh resolution for each field solution used 145 by 145 mesh lines. All programs were written by the author and are part of the KEOS package, which are reported in detail in A. Khusheed, The Finite Element Method in Charged Particle Optics, (Kluwer Academic Press, Boston, USA, 1999). The accuracy of the simulation was continually checked by repeating all results with finer numerical meshes and smaller trajectory step sizes, ensuring that the final simulated parameters such as rms trace width did not change significantly (by less than 1%).
At present, the detection systems of the Scanning Electron Microscope (SEM), Scanning Helium Ion Microscope (SHIM) or Focused Ion Beam (FIB) are not generally designed to capture the energy spectrum of the ions/electrons scattered from the sample. Their output signals are formed by secondary electrons and backscattered electrons/ions, which are usually detected separately. However, the energy spectra of these scattered particles contain valuable information about the sample under study. The shape of the emitted secondary electron spectrum is related to the sample's work function, which is very useful for applications such as PN junction doping concentration mapping. The backscattered ion/electron spectrum changes significantly with atomic number. Combining this kind of information with a scanning ion/electron microscope's normal imaging mode of operation, would obviously make it a much more powerful analytical tool for nano-scale inspection. BSE spectral results disclosed herein demonstrate that a second-order focusing toroidal spectrometer according to the present invention can be used to enable a conventional SEM to acquire quantitative BSE material contrast information.
Further simulations have shown that an accelerating pre-focusing lens improves the energy resolution for a given entrance angular spread by an order of magnitude (0.02% for ±6° entrance angular spread).
In these simulations, all field distributions and electron trajectory ray paths were simulated using Lorentz-2EM, a hybrid software that combines boundary element and finite element techniques. The boundary element method avoids well-known mesh generation/interpolation problems of the finite element method, especially difficult for curved boundaries. On the other hand, the finite element method was used for non-linear field solutions, such as those that arise in the presence of magnetic saturation, which are difficult to solve directly by boundary element methods. Both numerical techniques were coupled together, utilizing their relative strengths. In addition, an adaptive segment technique varied the density of charge segments on conductor surfaces, refining it according to local field strength. The subsequent improvement on field accuracy and shortening of trajectory run times for a given number of charge segments, allowed for modeling of problems of greater complexity. The software was able, for instance, to simulate electrostatic structures that are very small, and embedded in much larger conductor layouts. In the present context, this feature was used to plot accurate direct trajectory paths through an aperture slit, microns in size, placed within the fringe fields of a spectrometer measuring many centimeters. The use of a 5th order Runge-Kutta method in which the trajectory step-size varies according to local truncation error also helped in making this kind of problem much easier to simulate. The accuracy of all simulations were continually checked by repeating all results with smaller boundary segments and trajectory step sizes, ensuring that important ray tracing parameters, such as the rms value for the final focal point size at the spectrometer exit did not change significantly (by less than 1%).
To summarize, a toroidal electron energy spectrometer according to the present invention captures electrons in the full 2π azimuthal angular direction while at the same time having second-order focusing optics. Simulation results based upon direct ray tracing predict that the relative energy resolution of a spectrometer according to the present invention will be 0.146% and 0.0188% at input angular spreads of ±6° and ±3° respectively, which is comparable to the theoretically best resolution of the Cylindrical Mirror Analyzer (CMA), and an order of magnitude better than existing toroidal spectrometers. Also predicted for the spectrometer is a parallel energy acquisition mode of operation, where the energy bandwidth is expected to be greater than ±10% (20% total) of the pass energy. A spectrometer according to the present invention can allow for retardation of the pass energy without the need to incorporate auxiliary lenses.
A spectrometer according to the present invention combined with a pre-focusing electrostatic lens, is predicted to have a relative energy resolution of 0.02% and 0.088% for emission angular spreads of ±6° and ±10° respectively, corresponding to a transmittance of around 20% and 34%.
Other features and advantages of the present invention will become apparent from the following description of the invention which refers to the accompanying drawings.